Conjugate[] isn't working for me

Hi!
Conjugate is not working like I expect on certain exponentials:

What do I misunderstand?

Thanks!
Chris

It can be a struggle to get the exact form you have in mind. Here is a way for your second example:

Conjugate[E^(-I*w*x) + E^(-4*I*w*x)] // ComplexExpand // TrigToExp

What do I misunderstand?

Nothing! Simply try FullSimplify[] instead of Simplify[].

Henrik and Gianluca:

Thanks! Both solutions worked like a champ.

I appreciate your help as I get up to speed on Mathematica.

Chris